There is no "registration" required unless you are building an SBR.
All (Federal) Title I rifles have to be over 26" overall length AND over 16" barrel length. But your title asks about pistols, not rifles.
The only AW bans in IL are city or county bans in the Chicago area. There is no state level AW regulation. Are you in the Chicago area? There are also magazine bans in some of those Chicago-area cities. One odd restriction in the city of Chicago is that laser aiming pointers are prohibited.
In theory any portion of AW bans regulating handguns were voided by their concealed carry law, but there is no caselaw on that yet.
If you buy a lower you don't state that it's for anything, and it would be irrelevant in any event. Stripped receivers are just that, and transfer as "other" on a 4473.